Physics 263

Experiment 7

Wave Optics

In this laboratory, we will perform two experiments on “wave” optics.

1 Double Slit Interference

In two-slit interference, light falls on an opaque screen with two closely spaced, narrowslits. As Huygen’s principle tells us, each slit acts as a new source of light. Since theslits are illuminated by the same wave front, these sources are in phase. Where the wavefronts from the two sources overlap, an interference pattern is formed.

Figure 1: Double slit interference experiment

Interference maxima will occur when the overlaping waves are in phase. This happenswhen the path difference from the slits to the observation point is an integral number ofwavelengths of the light. If d is the slit separation, then the path difference, as shown inFigure 1 is d sin θ So

sin θmax = mλ/d (1)

in which m is an integer.In this experiment we will measure the angles θmax for light of wavelength 650 nm,

and slits of known separation 0.25 mm.

In the “ideal” two-slit interference experiment, the width of each of the two slits ismuch smaller than a wavelength of light. This makes each slit produce an approximatelyisotropic distribution, i.e. the same in all directions. But in order to produce enough

light for you to see, this apparatus has slits which are large enough that their angulardistribution is not isotropic; each slit produces an intensity pattern which corresponds todiffraction by a single narrow slit. The overall result you will see is the combination ofthese patterns, shown in Figure 2.

Figure 2: Intensity and diffraction “envelope” vs. angle for a similar setup.

Procedure

1. Set up the diode laser and the slit set as shown in Figure 3.

Figure 3: Diode laser and slit set arrangement.

Then set up the white viewing screen at the far end of the optical “bench”, as shownin Figure 4.

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Figure 4: Overall apparatus setup for double slit interference.

2. Turn on the laser, and adjust the beam and rotate the slit wheel until the beamhits the double slit set which has separation (d) of 0.25 mm, and width 0.04 mm.Do not look directly into the laser.

3. Observe the interference pattern on the screen. You will probably need the roomlights off for this. Fasten a piece of paper to the screen, and mark the paper atmany maxima on each side of the central maximum.

4. Measure the distances from the central maximum (y = 0) to the different maxima,∆ym. Also measure the distance from the slit to the screen. Use these to figure outthe angles θmax m. Measure ∆ym and find θmax m for maxima both above and belowthe the central maximum (m = 0).

5. Use Equation 1 to predict the same set of angles. Compare with the measurements:list or plot the differences between measured and predicted θ’s.

2 Linear Polarization

Light is a transverse wave; the electric and magnetic field vectors are always oriented in adirection perpendicular to the direction of propagation (see Figure 4a). Light is linearlypolarized when the electric field vector has a fixed orientation in the transverse plane.By convention the direction of polarization is taken to be the direction of the electricfield. Light us unpolarized when the direction of the electric field changes rapidly andrandomly with time. Light from incandescent and fluorescent lamps is unpolarized.

Unpolarized light may be polarized by filters, by reflection and by scattering. Filters,usually called “Polaroid” filters polarize light by absorbing out all the light except thatwhich has the E-vector pointing along a specific direction (to within a sign.) This directionis called the “pass axis”.

The components of the electric field in a direction perpendicular to this axis is absorbedby the polaroid material. If polarized light with electric field Einc is incident on a polaroidfilter, then the electric field of the transmitted light is then just the component of Einc

along the direction of the pass axis:

Etrans = Einc cos φ (2)

in which φ is the angle between the pass axis and Einc.

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If the incident light has randomly oriented electric fields, the transmitted light ispolarized along the pass axis. Since the light intensity, I is proportional to the time-average of E2, Equation 2 tells us that

Itrans = Iinc cos2 φ (3)

This result (a theorem) is known as Malus’ Law.1

The effect of two sequential polarizing filters is illustrated in Figure 5. The first filterpolarizes the incoming unpolarized light. The light intensity transmitted by the secondfilter obeys Equation 3, in which φ is the angle between the pass axes of the two filters.If the filters are “crossed”, i.e. φ = 90◦, no light is transmitted.

Figure 5: Unpolarized light incident on a set of two polarizing filters.

Procedure

1. Set up the diode laser, the two polarizers and the light sensor with aperture disk asshown in Figure 6.

1Linearly polarized light is also sometimes called “plane polarized” light. There is another type ofpolarization, circular polarization, in which the electric field vector rotates in the transverse plane. Wewill not study this type in this laboratory.

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Figure 6: Apparatus for 2-polarizer experiment.

2. Set the open circular aperature in front of the light sensor. Plug the sensor outputinto Channel A of the Pasco interface.

3. Open the Data Studio program; select a new experiment and select the light sensor.Select the digital display for the output of this sensor.

4. Turn on the light source, and adjust the laser light spot so that is is directed throughthe filters and at the light sensor aperature.

5. With both polarizers set to 0◦, look at the digital light sensor output. Adjust thesensor gain until this value is above at least 50%.

6. Take readings at angles φ from 0◦ to 90◦ in 10◦ intervals. (Leave the filterclosest to the light source at 0◦ and change the other.) Record the angleand the intensity in a spreadsheet.

7. Plot I vs. cos2 φ. Fit the result to a straight line.

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